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Question:

The greatest value of c∈ R for which the system of linear equations x-cy-cz=0, cx-y+cz=0, cx+cy-z=0 has a non-trivial solution is:

0

1/2

-1

2

Solution:

Correct option is A. 1/2
For non-trivial solution D=0
|1 -c -c|
|c -1 c|=0 => 2c³ - 3c - 1 = 0 => (c+1)²(2c-1) = 0
|c c -1|
Therefore, Greatest value of c is 1/2